In 2007, a mathematical model of the physarum polycephalum, which is the original physarum polycephalum inspired algorithm (OPPA) was proposed [1]}. In the OPPA, the tube-liked body of the physarum polycephalum is considered as a network with the growing point and the food source serving as the starting point and ending point, respectively; the Poiseuille flow is adopted to model the flow flowing through the tube; the conservation law of flux (also called continuity of flux) is obeyed using network Poisson equation [2]}. At the core of the OPPA is the use of a novel adaptive equation to model the dynamics of tube thickness. By using the techniques mentioned above, the OPPA perfectly models the path-finding behavior of the amoeboid organism and was then applied to solve the minimum-risk path-finding problems [1]} and adaptive network design problems [2]}. The effectiveness of the OPPA has been mathematically proven. Bonifaci et al. provided a mathematical proof of the convergence of the OPPA on the shortest path problems [5]} and provided the time complexity bounds [6]}. Karrenbauer et al. developed on the former proof and proposed a more general proof for the effectiveness of the OPPA [7]}.
